Preventing MRSA by cleaning a gym is pretty hard though. People carry staph bacteria, including methicillin resistant strains, on their skin and in their nasal passages without effect. Unless it is a health care environment, I think the steps a facility would have to take to ensure it was sterile every day would be overkill.
I have gotten a staph infection (not meth-resistant, this was probably 04 or 05). I probably picked it up at the gym. It would have been preventable with some foresight though. I still never use commercial hand sanitizer; I do wash my hands.
It is more effective IMO for individuals to take steps to reduce their chances of being affected by this, but if you aren't immuno-compromised and the site of the infection is the surface of the skin (i.e. you didn't have surgery in an environment that wasn't sterile causing an internal infection), strains of staph aren't as scary as you might believe. I am not trying to minimize the issue because it is still a serious public health hazard, but those are generally the more major risks for very serious cases.
1. wash hands and take a shower soon after practice. Wash skin and hair (doesn't need to be "99% germ killing" type solution), normal soap and warm water should do.
2. Cover ALL open wounds on the surface of the skin especially on the feet. The entry site for my infection was an area where a flip flop had rubbed several layers of skin off (kind of like a bad rip on my foot). I had it covered poorly and decided not to bother a couple hours into practice.
3. Minimize skin to skin contact. Completely avoid skin to skin contact with wounded areas or used bandages.
4. Immediately (immediately!) seek medical care for sudden and unexplained spreading pain originating from the site of a wound. I cannot emphasize this enough. Infections that spread up the bloodstream spread fast and depending on the site and the strain they can affect organs within a day or so. Currently even MRSA is being successfully treated if caught early. It is very important to be aware of what a MRSA infected site looks like and seek treatment if you suspect it or any other serious spreading infection.
But to be honest I don't worry that much about it. I had open cuts on both my heels today from shoes and I didn't even think about it until now (and I worked out today with bare feet). I'm not trying to be flippant about it, but I did gymnastics, high school gymnastics, school gym classes day in and day out for years. I just don't worry about it that much in the scheme of things. I have had one staph infection. Furthermore, I am the ONLY person I know who has had a staph infection. OTOH, I have known multiple people with ringworm. While the rise of meth-resistant strains of staph is a concerning public health hazard, most of the concern was over the resistance, not over this being an extremely frequent occurence in any given place. It's certainly something to be aware of but I don't think you can really sterilize a gym and I don't think that's necessary at this point. Washing and covering openings on the skin should be enough at this point. Last year all high school athletes in my county had to see a MRSA video and go through this whole thing, but this was basically the extent of their recommendation. Take a shower and cover wounds.